Alternating-direction implicit method: Difference between revisions

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Rescuing 1 sources and tagging 0 as dead.) #IABot (v2.0.9.5
Adding brackets around the definition of e_p to match the notation used for the lattice point instead of just the numbers 10 and 01
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and <math>\delta_p^2</math> is the central second difference operator for the ''p''-th coordinate
: <math>\delta_p^2 u_{ij}=u_{ij+e_p}-2u_{ij}+u_{ij-e_p}</math>
with <math>e_p=10(1,0)</math> or <math>01(0,1)</math> for <math>p=x</math> or <math>y</math> respectively (and <math>ij</math> a shorthand for lattice points <math>(i,j)</math>).
 
After performing a [[Von Neumann stability analysis|stability analysis]], it can be shown that this method will be stable for any <math>\Delta t</math>.